Lie Group Control Architectures for UAVs: a Comparison of SE2(3)-Based Approaches in Simulation and Hardware

This paper presents the integration and experimental validation of advanced control strategies for quadcopters based on Lie groups. We build upon recent theoretical developments on SE2(3)-based controllers and introduce a novel SE2(3) model predictive controller (MPC) that combines the predictive capabilities and constraint-handling of optimal control with the geometric properties of Lie group formulations. We evaluated this MPC against a state-of-the-art SE2(3)-based LQR approach and obtained comparable performance in simulation. Both controllers where also deployed on the Quanser QDrone platform and compared to each other and an industry standard control architecture. Results show that the SE_2(3) MPC achieves superior trajectory tracking performance and robustness across a range of scenarios. This work demonstrates the practical effectiveness of Lie group-based controllers and offers comparative insights into their impact on system behaviour and real-time performance

Decentralized Swarm Control via SO(3) Embeddings for 3D Trajectories

This paper presents a novel decentralized approach for achieving emergent behavior in multi-agent systems with minimal information sharing. Based on prior work in simple orbits, our method produces a broad class of stable, periodic trajectories by stabilizing the system around a Lie group-based geometric embedding. Employing the Lie group SO(3), we generate a wider range of periodic curves than existing quaternion-based methods. Furthermore, we exploit SO(3) properties to eliminate the need for velocity inputs, allowing agents to receive only position inputs. We also propose a novel phase controller that ensures uniform agent separation, along with a formal stability proof. Validation through simulations and experiments showcases the method's adaptability to complex low-level dynamics and disturbances.

Emergent Structure in Multi-agent Systems Using Geometric Embeddings

This work investigates the self-organization of multi-agent systems into closed trajectories, a common requirement in unmanned aerial vehicle (UAV) surveillance tasks. In such scenarios, smooth, unbiased control signals save energy and mitigate mechanical strain. We propose a decentralized control system architecture that produces a globally stable emergent structure from local observations only; there is no requirement for agents to share a global plan or follow prescribed trajectories. Central to our approach is the formulation of an injective virtual embedding induced by rotations from the actual agent positions. This embedding serves as a structure-preserving map around which all agent stabilize their relative positions and permits the use of well-established linear control techniques. We construct the embedding such that it is topologically equivalent to the desired trajectory (i.e., a homeomorphism), thereby preserving the stability characteristics. We demonstrate the versatility of this approach through implementation on a swarm of Quanser QDrone quadcopters. Results demonstrate the quadcopters self-organize into the desired trajectory while maintaining even separation.